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- Volume 32, Issue 4, 1984
Geophysical Prospecting - Volume 32, Issue 4, 1984
Volume 32, Issue 4, 1984
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TUTORIAL MINIMUM PHASE FOR CONTINUOUS TIME AND DISCRETE TIME FUNCTIONS*
By E. EISNERAbstractThe concept of minimum phase is clarified for geophysicists by collecting in one place the properties of minimum phase functions. The “earliest energy arrival” property in the time domain, the “minimum phase‐slope property” in the frequency domain, and of the role of causal all‐pass filters are demonstrated. The emphasis is placed on keeping the mathematics within the realm familiar to geophysicists and on making clear the somewhat imperfect match between physical continuous time functions and their associated discrete time representations.
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FRACTURES AS CONDUCTING DYKES AND CORRESPONDING TWO‐DIMENSIONAL MODELS*
By A. ÁDÁMAbstractA statistical treatment of MT data from the Pannonian Basin, Hungary, based on the distortion theory of the S‐effect suggests that the local increase in crustal conductivity is connected with deep fractures.
Field model measurements have recently been carried out in a shallow, quasi two‐dimensional basin of well known tectonics using MT station distances of 1–3 km. The results of the investigation and numerical modelling of near surface distortions, support the idea that deep fractures (faults) contain the conducting formations. According to 2‐D model computations, several conducting dykes at considerable depths can cause anomalies which are indiscernible from an anomaly due to a conducting layer. The significance of these results is discussed from the point of view of geothermal energy exploitation.
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RESISTIVITY AND MAGNETIC SURVEYS IN GROUNDWATER PROSPECTING IN VOLCANIC AREAS—CASE HISTORY MAAR OF BEAUNIT, PUY DE DOME, FRANCE*
Authors M. AUBERT, G. CAMUS and C. FOURNIERAbstractVolcanic maar structures sometimes contain important groundwater reserves. The volcanic formations of the Beaunit maar have a much higher magnetization than their granite substrata. The structure of the maar and its volcanoclastic infill can therefore be defined by magnetic surveying and resistivity soundings. Resistivities of the geological formations present in the Beaunit maar are comparable to those recorded in other volcanic systems. The geophysical data, confirmed by drilling tests, contain useful information on the hydrogeological regime of the volcanic system under investigation.
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RESOLUTION ENHANCEMENT OF WELL LOG AND SEISMIC DATA*
Authors A. G. MICHETTE, A. M. DARLING, M. A. FIDDY, W. A. WARD and E. FRANKLINAbstractA new method with general applications for seismic data is presented for spectral extrapolation. The method gives a restored image that is optimum in the sense of minimum norm and can be adapted to incorporate any constraints on the reconstruction. As an illustration of the technique it is first applied to a synthesized (noise‐free) image. Then it is shown that enhancement of a density log (run in a hole drilled entirely in Coal Measures rocks) is possible using constraints taken from the geologist's log. A synthetic trace with significantly improved event arrival times and general character is obtained.
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LIMITS OF STRUCTURAL INVERSION OF SEISMIC HORIZONS*
Authors D. BILGERI and A. CARLINIAbstractTime horizons can be depth‐migrated when interval velocities are known; on the other hand, the velocity distribution can be found when traveltimes and NMO velocities at zero offset are known (wavefront curvatures; Shah 1973).
Using these concepts, exact recursive inversion formulae for the calculation of interval velocities are given. The assumption of rectilinear raypath propagation within each layer is made; interval velocities and curvatures of the interfaces between layers can be found if traveltimes together with their gradients and curvatures and very precise VNMO velocities at zero offset are known.
However, the available stacking velocity is a numerical quantity which has no direct physical significance; its deviation from zero offset NMO velocity is examined in terms of horizon curvatures, cable length and lateral velocity inhomogeneities.
A method has been derived to estimate the geological depth model by searching, iteratively, for the best solution that minimizes the difference between stacking velocities from the real data and from the structural model.
Results show the limits and capabilities of the approach; perhaps, owing to the low resolution of conventional velocity analyses, a simplified version of the given formulae would be more robust.
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VSP INTERVAL VELOCITIES FROM TRAVELTIME INVERSION*
More LessAbstractA principal use of the vertical seismic profile (VSP) is to determine the variation of seismic velocity with depth. Presented here is a discussion of the errors involved with the time picks of a VSP survey and several methods currently used to calculate a velocity section from these time picks. Another technique is proposed, based on the least‐squares inversion of the traveltimes, to arrive at a better estimate and statistical description of the velocity section. This technique uses the Levenberg‐Marquardt damped least‐squares formulation and ray tracing through a horizontally‐layered medium to iteratively refine the velocity section. The accuracy and robustness of the procedure are investigated by inverting noisy traveltime curves and comparing these results to the original model velocity section. Agreement is found to be good. One interesting feature of the inverse procedure is that, for certain geometries, it can resolve a few velocity layers, even though there are no measurements made inside those layers. Three actual VSP surveys are analyzed and compared to their corresponding sonic logs. In two of the surveys, it appears that there is some velocity dispersion. Velocity changes associated with gas saturation are evident on one of the surveys.
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INFLUENCE OF VELOCITY ERRORS ON THE FOCUSING ASPECTS OF MIGRATION*
Authors D. DE VRIES and A. J. BERKHOUTAbstractIn migration procedures, the velocity profile of the subsurface is the most important input information. Since, in general, this information is only approximately known, errors in the migration output due to errors in the velocity input occur in all practical applications. In migration, velocity errors and depth errors can be interchanged. This interchange property is perfect in the paraxial approximation. From this result it follows that migration with incorrect velocities may still yield correctly migrated data if the imaging principle is modified. This attractive property can be used in the stripping version of migration (recursive migration).
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IN‐SEAM SEISMIC LOVE WAVE SCATTERING MODELED BY THE FINITE ELEMENT METHOD*
Authors M. W. ASTEN, L. A. DRAKE and S. EDWARDSAbstractThe dynamic finite‐element method allows frequency‐dependent reflection and transmission coefficients to be computed for Love waves scattered by two‐dimensional inhomogeneities in coal seams.
Clean faults of zero hade angle show a throw‐dependent cross‐over frequency in reflection spectra, and throw‐dependent conversion from fundamental to first higher mode energy in transmission spectra. Oblique faults show mode conversion in reflection spectra which is relatable to the fault hade angle by simple Huygens‐theory models. Thin fracture zones or dykes normal to the seam show a reflection maximum when thickness of the zone is of order one quarter of the seam wave wavelength.
Published field data from two known faults and a dyke are compared with the modeling results and support the belief that broad‐band seam‐wave data are capable of characterizing a seam discontinuity (throw, hade angle, dyke thickness) as well as locating it. Development of such procedures will require extensions to existing field practice and processing.
This research was funded in part by the National Energy Research Development and Demonstration Council of Australia. The authors thank The Broken Hill Proprietary Company Limited for permission to quote from company case histories.
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THE USE OF SEISMIC SHEAR WAVES AND COMPRESSIONAL WAVES FOR LITHOLOGICAL PROBLEMS OF SHALLOW SEDIMENTS*
Authors H. STÜMPEL, S. KÄHLER, R. MEISSNER and B. MILKEREITAbstractFrom a great variety of in situ shear wave experiments, i.e., reflection, refraction and borehole surveys in the shallow sediments of the north German plains, several specific properties have been derived. Shear waves (S) differ from compressional waves (P) in that:
- 1 they are not affected by the degree of water saturation. Thus, they provide a better correlation between the velocity Vs and (solid) lithology;
- 2 they generally have lower frequencies, but shorter wavelength and, hence, a better resolution of thin layers;
- 3 they have lower absorption Qs−1 and hence a better penetration in partially saturated and gas‐containing sediments than P‐waves.
Correlations have been established between Vs and the confining pressure and between reduced Vs values and several lithological parameters like the grain size of sandy material. More lithological and hydrological information is obtained by using S‐ and P‐wave surveys along the same profile. The best information on a sedimentological structure is obtained by the simultaneous observation of Vs, Vp, Qs and Qp.
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INTERACTION BETWEEN AIRGUNS*
Authors S. VAAGE, B. URSIN and K. HAUGLANDAbstractIn the design of linear airgun arrays the interaction between the airguns is usually neglected. We review the different formulae which have been proposed for the minimum separation between airguns at which the interaction is negligible. These formulae can all be approximated by a linear function of a single variable.
We have analyzed a large number of measurements in order to establish the amount of interaction between two airguns of various volumes at different pressures and depths. The resulting far‐field signature has been measured and compared with the sum of the signatures from the two airguns measured in the same experimental situation. The changes in primary pulse amplitude, bubble period and primary/bubble peak‐to‐peak amplitude ratio were computed from the measurement data as a function of airgun separation, chamber volume, chamber pressure and airgun depth. The influence of a waveshape kit was investigated, and the effects of interaction and the effects of using a waveshape kit were compared.
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GUIDED LOW‐FREQUENCY NOISE FROM AIRGUN SOURCES*
Authors B. L. N. KENNETT and A. J. HARDINGAbstractThe presence of the water layer in marine seismic prospecting provides an effective waveguide for acoustic energy trapped between the sea‐bed and the sea‐surface. This energy persists to large ranges and can be the dominant early feature on far‐offset traces. On airgun records, there is commonly a lower frequency set of arrivals following the water‐trapped waves. These arrivals are not as obvious with higher frequency watergun sources. By using a combination of intercept‐time/slowness (τ—p) mapping on observational data and theoretical modelling, we are able to identify the origin of the events. If a very rapid increase in a seismic wavespeed occurs beneath the sea‐bed sediments, a new waveguide is formed bounded by the sea surface and this transition zone. The low frequency waves are principally guided within this thicker waveguide. Numerical filtering in the τ—p domain followed by trace reconstruction is very effective in removing the low frequency noise.
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STATISTICAL EVALUATION OF MT AND AMT METHODS APPLIED TO A BASALT‐COVERED AREA IN SOUTHEASTERN ANATOLIA, TURKEY*
Authors O. M. ILKISIK and A. G. JONESAbstractThe efficacy of the magnetotelluric and audiomagnetotelluric (MT/AMT) methods for detailing the structure of a hypothetical geological section is investigated by using the singular value decomposition (SVD) technique. The section is representative of southeastern Turkey, which is mostly covered by basalt and is a prime area for oil exploration. One of the geological units, the Germav shale at a depth of 600 m, is a problem layer for electromagnetic surveys because of its very low resistivity (on average 3 Ωm) and highly variable thickness across the area (200–900 m). In the MT frequency range (0.0004–40 Hz) its total conductance—or, since its resistivity is known from resistivity log information, its thickness—is the best resolved model parameter. The total depth to the Germav shale and the resistivity of the Cambrian/Precambrian basement are the marginally resolved parameters. In the AMT frequency range (4–10000 Hz) the resistivity of the surface basalt layer strongly affects the resolution of the other, less important, model parameters which are the total depth to the Germav shale and the total conductance of the Germav shale. The errors in the measurements determine the number of model parameters resolvable, and are also important for interpretation of the geological model parameters to within a desired accuracy.
It is shown that statistical evaluation of the MT and/or AMT interpretations by using an SVD factorization of the sensitivity matrix can be helpful to define the importance of some particular stage of the interpretation, and also provides a priori knowledge to plan a proposed survey. Arrangements of MT and AMT observations, together with some Schlumberger resistivity soundings, on a large grid will certainly provide three‐dimensional detailed information of the deep geoelectric structure of the area.
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A FIELD EXAMPLE OF THE USE OF ANISOTROPY PARAMETERS DERIVED FROM RESISTIVITY SOUNDINGS*
Authors M. J. S. MATIAS and G. M. HABBERJAMAbstractIn areas where steep dips are encountered conventional practice in resistivity work has involved orienting arrays favourably in relation to the geological strike. In concealed conditions, however, the geological strike may not be known; moreover, strike may change with depth. Considerable advantage is to be gained, in such circumstances, by the use of crossed square arrays in that these yield orientationally insensitive resistivity measurements and also allow strike determinations and measurements of the effective vertical anisotropy.
Two traverses of crossed square array observations are presented, together with one deeper sounding. The results show that, in favourable circumstances, reliable data on concealed strike directions can be obtained, and that the anisotropy findings greatly assist the subsequent interpretation. Model results pertinent to the field material are presented and discussed.
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NOMOGRAMS TO INTERPRET CRONE PEM DATA USING A DIPPING SHEET MODEL*
Authors S. S. RAI and S. K. VERMAAbstractThe response of a rectangular plate to the Crone PEM system has been investigated for different values of depth, dip and conductance parameters. The conductance aperture diagram is presented to estimate the conductance and depth to the top of a vertical sheet. Information regarding dip and depth may be obtained using the appropriate nomogram.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)